Solve for x, y, z
x=3
y=-18
z=17
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x=-y-z+2
Solve x+y+z=2 for x.
6\left(-y-z+2\right)+4y+5z=31 5\left(-y-z+2\right)+2y+2z=13
Substitute -y-z+2 for x in the second and third equation.
y=-\frac{1}{2}z-\frac{19}{2} z=-1-y
Solve these equations for y and z respectively.
z=-1-\left(-\frac{1}{2}z-\frac{19}{2}\right)
Substitute -\frac{1}{2}z-\frac{19}{2} for y in the equation z=-1-y.
z=17
Solve z=-1-\left(-\frac{1}{2}z-\frac{19}{2}\right) for z.
y=-\frac{1}{2}\times 17-\frac{19}{2}
Substitute 17 for z in the equation y=-\frac{1}{2}z-\frac{19}{2}.
y=-18
Calculate y from y=-\frac{1}{2}\times 17-\frac{19}{2}.
x=-\left(-18\right)-17+2
Substitute -18 for y and 17 for z in the equation x=-y-z+2.
x=3
Calculate x from x=-\left(-18\right)-17+2.
x=3 y=-18 z=17
The system is now solved.
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